ON THE EXPANSION OF COMBINATORIAL POLYTOPES

Strong expansion properties have been established for several classes of graphs that can be expressed as the 1-skeletons of 0-1 polytopes. These include graphs associated with, matchings, order ideals, independent sets, and balanced matroids (e.g. for the graphic matroid). The question whether these are examples of a more general phenomenon has been raiseD: ''Do all 0-1 polytopes have cutset expansion at least 1 ?'' A positive answer to the above question (even in weaker or more special form), implies efficient randomized algorithms to approximate a vast class of NP-hard counting problems.